TY  - JOUR
T1  - A two-step approach to ratio and regression estimation of finite population mean using optional randomized response models
AU  - Gupta, Sat
AU  - Kalucha, Geeta
AU  - Shabbir, Javid
PY  - 2016
DA  - December
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1819
EP  - 1830
VL  - 45
IS  - 6
LA  - en
AB  - We propose a modied two-step approach for estimating the mean of asensitive variable using an additive optional RRT model which allowsrespondents the option of answering a quantitative sensitive questiondirectly without using the additive scrambling if they find the question non-sensitive. This situation has been handled before in Gupta etal. (2010) using the split sample approach. In this work we avoid thesplit sample approach which requires larger total sample size. Instead,we estimate the finite population mean by using an Optional Additive Scrambling RRT Model but the corresponding sensitivity level isestimated from the same sample by using the traditional Binary Unrelated Question RRT Model of Greenberg et al. (1969). The initialmean estimation is further improved by utilizing information from anon-sensitive auxiliary variable by way of ratio and regression estimators. Expressions for the Bias and MSE of the proposed estimators(correct up to first order approximation) are derived. We compare theresults of this new model with those of the split-sample based OptionalAdditive RRT Model of Kalucha et al. (2015), Gupta et al. (2015) andthe simple optional additive RRT Model of Gupta et al. (2010). We seethat the regression estimator for the new model has the smallest MSEamong all of the estimators considered here when they have the samesample size.
KW  - Auxiliary Information
KW  - Mean square error
KW  - Optional randomized response technique
KW  - Ratio estimator
KW  - Regression estimator
KW  - Unrelated Question RRT Model
CR  - .
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UR  - https://dergipark.org.tr/en/pub/hujms/article/524432
L1  - https://dergipark.org.tr/en/download/article-file/644829
ER  -